Results 21 to 30 of about 1,512 (69)

Embedded constant curvature curves on convex surfaces

, 2011
We prove the existence of embedded closed constant curvature curves on convex surfaces.Comment: 6 ...
Rosenberg, Harold, Schneider, Matthias
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Coding of hypersurfaces in Euclidean spaces by a constant vector

Open Mathematics
An nn-dimensional Riemannian manifold (Nn,g)({N}^{n},g) isometrically immersed in Euclidean space Rn+1{R}^{n+1} with unit normal ζ\zeta and shape operator SS, for a fixed constant unit vector a→\overrightarrow{{\bf{a}}} in Rn+1{R}^{n+1} induces a vector
Deshmukh Sharief, Guediri Mohammed
doaj   +1 more source

A Remark on Soliton Equation of Mean Curvature Flow

, 2003
In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension.
Ma, L., Yang, Y.
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Survey on real forms of the complex A2(2)-Toda equation and surface theory

Complex Manifolds, 2019
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop ...
Dorfmeister Josef F., Freyn Walter, Kobayashi Shimpei, Wang Erxiao   +3 more
doaj   +1 more source

Stable hypersurfaces with zero scalar curvature in Euclidean space

, 2016
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of ...
Alencar, Hilário, Carmo, Manfredo do, Neto, Gregório Silva   +2 more
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f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
Here we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold.
Hui Shyamal Kumar, Breaz Daniel, Mandal Pradip   +2 more
doaj   +1 more source

A geometric proof of the Karpelevich-Mostow's theorem

, 2007
In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit.
Di Scala, Antonio J., Olmos, Carlos
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Nonexistence of mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products

Advances in Nonlinear Analysis
Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions ...
Batista Márcio, Molica Bisci Giovanni, de Lima Henrique F., Gomes Wallace F.   +3 more
doaj   +1 more source

Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces

Complex Manifolds, 2019
An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded ...
Ohnita Yoshihiro
doaj   +1 more source

A generalization of Cartan's theorem on isoparametric cubics

, 2010
We give a generalization of the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation $|\nabla f|^2=9|x|^4$ must be rotationally equivalent to either $x_n^3-3x_n(x_1^2 ...
Tkachev, Vladimir G.
core   +1 more source